Given equation is
To find nature of roots , we need to find Discriminant,D =
now , from comparing equation with the general equation of quadratic form ,
We get , a = 4 , b = -12 , c = 9
Now finding discriminant , D = b^2-4ac substituting the values we get,
D = (-12)^2 - 4(4)(9)
=> D = 144-144 = 0
If D = 0 then the roots are rational and equal roots occur.
To find them we can use -b/2a , -b/2a
If D>0 then roots are real and unequal
If D<0 there are no real roots , complex roots (imaginary roots exist)
If D= 0 roots and real and equal.